Topological quantum materials (TQMs) have attracted intensive attentions recent years in the area of condensed matter physics due to their novel topologies and the promising application in quantum computing, spin electronics, and next generation of integrated circuits. The scanning tunneling microscope/spectroscope (STM/STS) is regarded as a powerful technique to characterize the local density of state with atomic resolution, which is ideally dedicated to the measurements of bulk-boundary correspondence of TQMs. In this review, recent research on the bismuth-based TQMs, including quantum-spin Hall insulators, three-dimensional weak topological insulators, high-order topological insulators, topological Dirac semimetals, and dual topological insulators, by STM/STS is focused on. The efficient methods of the modulation of the topological properties of the TQMs are introduced, such as interlayer interaction, thickness variation, and local electric field perturbation, and finally, the challenges and prospects for this field are discussed.